quantization, quantum entanglement, non-localilty of 'particles' in timeless physics ... In the previous text we have emphasized the importance of the standard dynamic horn torus as natural unit for metrisation and as source of quantization. It represents the complex number (1,1) which has the smallest possible absolute value within our model, because (1/n,1) in the interpretation 1/n rotation per 1 full revolution is the same as 1 full rotation per n revolutions, and (1,n) has bigger absolute value. So (1,1) remains the smallest reference for all other ratios, and there are no fractions of revolution and rotation - only integers! For this unit horn torus we determine, that one revolution represents Planck time and the circumference of a longitude (meridian) Planck length L_{P}, while the circumferential speed of revolution is light speed c, and one rotation represents Planck's reduced constant ħ. Could natural quantization be explained and illustrated in a simpler way? In the horn torus model a spatial point is defined as list of integer pairs (m,n), where n·L_{P} is the 'distance' to a certain particle in the universe, now represented by the longitude of one certain horn torus (its bulge circumference). All these horn tori of different sizes are nested into one another at one point, the singular center of every horn torus. Neighbouring spatial points differ in at least one value within the list. In this image all particles in the universe are represented in every spatial point with their respective horn torus, they all are nested, interlaced, entangled. All are connected somehow, having the possibility to interact by affecting (adding, subtracting, changing) their rotations m·ħ mutually, independent from their 'distance' and without obligatory need to travel this 'distance'. Can quantum entanglement and non-locality be explained and illustrated more simply? Not as simple, related to our associations of particles, that populate our imagined three-dimensional space and move there like small flying balls or 'wave packets', is the definition and description of elementary particles as geometrical figures and part of a comprehensive entity. Faculty of abstraction is challenged maximally. Trials of assistance are provided on many pages of this website (see sitemap and texts). Role players are manifold Lissajous figures on horn torus surfaces, e.g. 1:2, 2:1, 3:1, 4:1. Time does not flow, time rolls! All particles - all horn tori - roll along an imaginary line, which is tangent to all tori and symmetry axis of the whole system. This line acts as physical time for the particles. We have two directions of rolling, what corresponds to time forward and time backwards, but only one direction is realized, when the horn tori shall keep their common point on the line. We now easily discover, that horns of very big tori, which are manifestation of particles in (nearly) infinite distance, create exactly the same line, that we have called time. Conclusion: we don't need time as an independent dimension. Its relevance is reduced to a simplifying auxiliary physical variable and to a term of pure human psychological perception. t is no longer abbreviation for elapsed time but for all revolving tori's travelled distance on their common tangent. it from bit ?? • animation |